Relay Network Endpoint Guarantee

A telecom engineer is auditing a mesh of n numbered relay stations connected by m one-way transmission links. A link from station u to station v means a message currently at u may be forwarded on to v; a station with no outgoing links is a terminal station where a message can go no further. Starting from a fixed source station src, a message may be forwarded along any sequence of links its handlers choose, and different handlers may make different choices at every station that offers more than one outgoing link -- the engineer cannot control which one is taken. The network passes the audit for a given destination station dst only if every such forwarding sequence starting at src is guaranteed to eventually stop at a terminal station, and that terminal station is always exactly dst -- no sequence may run forever by looping back through stations it already visited, and no sequence may dead-end at any station other than dst.

Determine whether the network passes the audit for the given src and dst.

Input format

• Line 1: two integers n and m -- the number of stations and the number of links.
• Each of the next m lines contains two integers u v, a one-way link from station u to station v.
• Final line: two integers src dst.

Output format

• Print YES if every forwarding sequence starting at src is guaranteed to terminate at dst, otherwise print NO.

Constraints

• 1 <= n <= 2000
• 0 <= m <= 4000
• 0 <= u, v < n for every link (self-loops, i.e. u == v, are allowed)
• no two links in the input have the same (u, v) pair
• 0 <= src, dst < n

4 4
0 1
0 2
1 3
2 3
0 3

YES

4 4
0 1
0 3
1 2
2 1
0 3

NO